Analysis and Design of a Class of Limiter Schemes in Presence of Physical Diffusion

Abstract

In order to solve the advection-diffusion transport equations (ADTE), many flux-limiting schemes have been proposed. In most cases, monotony conditions for these schemes ignore the process of the physical diffusion. In this paper, we propose new flux-limiter functions depending on the physical diffusion to ensure TVD (Total Variation Diminishing) constraints. These functions incorporate fully the physical diffusion so as to introduce the absolute minimum of numerical diffusion. We also present an application example to show that such TVD schemes are able to effectively reduce numerical dispersion even in the case where the convective process is of the same order as the diffusive one. This application example consists comparing the exact solution of ADTE to the numerical results of our new flux-limiter functions.